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Abstract

It is possible to reduce the diffraction peaks of a Spatial Light Modulator (SLM) by breaking the periodicity of the pixels shape. We propose a theoretical investigation of a SLM that would be based on a Voronoi diagram, obtained by deforming a regular grid, and show that for a specific deformation parameter the diffraction peaks disappear and are replaced with a speckle-like diffraction halo. We also develop a simple model to determine the shape and the level of this halo.

Figures (8)

Effect of an increasing randomness in the distribution of the cell centres. The initial square grid (a) has a pitch equal to d = 100µm. Pupil radius R=2mm. (c, e, g) : Associated Voronoi diagrams. The centres are moved according to a uniform distribution on a square of side α = ad with a = 0.5, a = 1.27 and a = 1.5. (b, d, f, h) : Corresponding histograms of wall orientations.

Fraunhofer diffraction patterns of the components of Fig.2 (a, c, e, g) and their horizontal cross sections through the center (b, d, f, h) for λ = 0.5µm, d = 100µm, l = 5µm and R = 2mm. The images as well as the cross-sections are shown in a logarithmic scale.

Comparison, at λ = 0.5µm, of the diffracted intensity computed by the slits cloud simulation (dotted line) and the theoretical model given by Eq. (3) (solid line) for N = 2000 slits with random orientations and positions according to a uniform distribution over [0,π] and
[−C2,C2]
. The length of all the slits is L = 100µm and the width : (a) l = 5µm, (b) l = 10µm, (c) l = 15µm and (d) l = 20µm.

Horizontal section of diffracted intensity pattern at λ = 0.5µm. Comparison between Voronoi simulations and the theoretical model given by Eq. (3). For all slits, l = 5µm. For the Voronoi simulations, the initial grid pitch is d = 100µm, a = √2 and R = 2mm. For Eq. (3), L = 100µm for all the slits.